Functional vector space

Recent developments in Functional Analysis witness the emergence of a new paradigm. Formal models seem destined to replace the standard taxonomical and descriptive approaches. In this paper we propose a new representation of the function space as a vector space. After discussing the rationale for the introduction of a formal architecture, we construct the vector space of functions (actions on flows) and individuate in physical and logical laws the ground for its generating vector basis. Finally, we discuss some key and unresolved issues and open several avenues for further research in the exciting and fast moving field of formal modelling of function spaces.